Question

A cylinder has a surface area of 312π ft.2. If its height is 20 ft., what is the measure of its radius?(1 point)

5.5 ft

6.5 ft

5 ft

6 ft

Answer 1

[AI-generated answer — Bot GPT 3.5]

6 ft

To find the radius of the cylinder, we use the formula for the surface area of a cylinder:

Surface Area = 2πrh + 2πr^2

Given the surface area is 312π ft^2 and the height is 20 ft, we can substitute those values into the formula:

312π = 2π(r)(20) + 2πr^2
312π = 40πr + 2πr^2

Now, we can simplify this equation:

312 = 40r + 2r^2
2r^2 + 40r - 312 = 0

To solve for r, we set the equation equal to zero and factor:

2r^2 + 40r - 312 = 0
r^2 + 20r - 156 = 0
(r + 26)(r - 6) = 0

Therefore, r = 6 ft

So, the measure of the radius of the cylinder is 6 ft.